Three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
(I).Some purses are keys.
(II). All lockers are keys.
(III).All keys are pins.
Conclusions:
I. Some pins are purses.
II. No pin is a purse.

​Statements:
​(I).Some purses are keys.
​(II). All lockers are keys.
​(III).All keys are pins.​

The least possible Venn diagram for the given statements is as shown below:

Conclusions:
(I) Some pins are purses.
From the statements:
Since "Some purses are keys" and "All keys are pins," the part of purses that overlaps with keys will also overlap with pins.
Hence, this conclusion logically follows.
(II) No pin is a purse.
This directly contradicts the first conclusion. Since we established that some pins are purses, this conclusion does not follow.

Thus, correct option is (a).​​